That isn't related to the screen, unless you replaced the whole radio. The SL02/03 part is just the actual literal display. The only thing that "could" cause the head unit to "boot faster" after a replacement might be the loss of the phantom presses during boot, or just the fact that the head unit ACTUALLY shut down for a bit, instead of just being asleep. (It seems counter intuitive, but that actually DOES help sometimes with computer systems.)
I skipped SL02 and went from SL01 to SL03. I did the "fix" on the SL01, and rode with it being "foggy" for like 6-9 months, so swapping to the "correct" SL03 from the "cleaned" SL01, the 03 is glossy AF. I don't remember the 01 being glossy, but I am not sure, because I don't really remember the 01 (even though I drove for like 4 years, but a concerning amount of that was while it was slowly melting.)